Textbook

Introduction

1. CARS

2. Psych/soc

3. Bio/biochem

4. Chem/phys

4.1 Translational motion, forces, work, energy, and equilibrium

4.2 Fluids in circulation of blood, gas movement, and gas exchange

4.2.1 Fluids and circulatory system fluids

4.2.2 Gas phase

4.3 Electrochemistry and electrical circuits and their elements

4.4 How light and sound interact with matter

4.5 Atoms, nuclear decay, electronic structure, and atomic chemical behavior

4.6 Unique nature of water and its solutions

4.7 Nature of molecules and intermolecular interaction

4.8 Separation and purification methods

4.9 Structure, function, and reactivity of bio-relevant molecules

4.10 Principles of chemical thermodynamics and kinetics, enzymes

Wrapping up

4.2.2 Gas phase

Achievable MCAT

4. Chem/phys

4.2. Fluids in circulation of blood, gas movement, and gas exchange

Gas phase

8 min read

Font

Discuss

Feedback

Absolute temperature, ( $K$ ) Kelvin scale

The absolute temperature scale is measured in Kelvin ( $K$ ). Its zero point is absolute zero, the lowest possible temperature, where no more thermal energy can be removed from a substance.

The Kelvin scale lines up with the Celsius ( $° C$ ) scale, using the relationship:

$K = ° C + 273$

So, water freezes at $273 K$ ( $0 ° C$ ) and boils at $373 K$ ( $100 ° C$ ).

The Fahrenheit ( $° F$ ) scale is still widely used in some regions, where:

$° F = 1.8 \times ° C + 32$

The Kelvin scale is especially important in science because it starts at the theoretical point of zero thermal energy.

Description	Celsius ( $C^{\circ}$ )	Kelvin ( $K$ )	Fahrenheit ( $F$ )
Surface of the sun	5600	5900	10100
Boiling point - water	100	373	212
Body temperature	37	310.2	98.6
Room temperature	20	293	68
Cool day	10	283	50
Freezing point - water	0	273	32

Pressure, simple mercury barometer

Pressure is the force exerted per unit area. It’s defined by:

$P = \frac{F}{A}$

where $F$ is the applied force and $A$ is the area over which the force acts.

At sea level, atmospheric pressure is about $101 k P a$ , which is equivalent to $1 a t m$ , and it decreases with increasing elevation. A mercury barometer measures atmospheric pressure by letting the atmosphere push a column of mercury upward. One end of the barometer is open to the air, while the other end is sealed, forming a vacuum.

The pressure is the weight of the mercury that is lifted ( $F$ ) divided by the cross-sectional area ( $A$ ) of the tube.
Standard barometers are calibrated so that $1 a t m$ raises the mercury to $760 mm$ , also written as $760 mm H g$ or $760 T orr$ .
When using the formula, make sure force is in Newtons ( $N$ ) and area is in square meters ( $m^{2}$ ). This gives pressure in Pascals ( $P a$ ).

Molar volume

The molar volume at 0 degrees Celsius and $1 a t m$ is $22.4 L / m o l$ . In other words, ideal gases occupy $22.4$ liters per mole of molecules under these standard conditions. (It’s $22.4 L$ per mole, not moles per liter.)

A mole contains about $6.02 \times 1 0^{23}$ particles, which is an enormous number of molecules and can take up a substantial volume. For example, air is mostly nitrogen; in its diatomic form ( $N_{2}$ ), nitrogen has a molar mass of about $28$ grams. Because air is light, a full mole of it occupies $22.4$ liters at standard conditions.

Ideal gas

An ideal gas is described by the kinetic molecular theory, which models a gas as a collection of point particles that move randomly and collide elastically with each other and with the container walls.

In an ideal gas, the molecular volume is negligible and there are no intermolecular forces. This behavior is a good approximation at low pressure and high temperature, where molecules are far apart. At high pressures and low temperatures, molecules are closer together, so intermolecular interactions and finite molecular volume become important, and the gas can eventually condense.

The behavior of an ideal gas is described by the ideal gas law:

$P V = n RT$

where $P$ is pressure, $V$ is volume, $n$ is the number of moles, $R$ is the gas constant, and $T$ is temperature.

This law leads to the combined gas law: when $n$ and $R$ are constant, the ratio $\frac{P V}{T}$ stays constant. From this relationship, you can derive:

Boyle’s law: $P_{1} V_{1} = P_{2} V_{2}$ at constant $T$
Charles’s law: $V \propto T$ at constant $P$
Avogadro’s law: equal volumes of gas at the same temperature and pressure contain equal numbers of moles

Kinetic molecular theory of gases

The kinetic molecular theory explains the behavior of gases and supports the ideal gas laws. It assumes that gas molecules:

are in constant, random molecular motion
experience no intermolecular forces
have negligible molecular volume
undergo perfectly elastic collisions, so the total kinetic energy stays constant during collisions

In this model, pressure comes from molecules colliding with the container walls. Because collisions occur randomly in all directions, the pressure is uniform throughout the container. Temperature measures the average kinetic energy of the gas molecules, so:

higher temperatures correspond to faster molecular speeds
lower temperatures correspond to slower molecular motion

Heat capacity at constant volume and at constant pressure

The heat capacity at constant volume is the heat required to raise a system’s temperature by one degree while keeping volume fixed. Because the volume doesn’t change, the system does no expansion work.

The heat capacity at constant pressure is the heat needed to raise the temperature by one degree while keeping pressure constant. Here, the system can expand, so some energy goes into expansion work. That’s why the constant-pressure heat capacity is higher than the constant-volume heat capacity. The difference between the two is explained by the work done against the surroundings.

Boltzmann’s constant is a fundamental value that links the average kinetic energy of individual particles to the macroscopic temperature of a system. It connects microscopic particle behavior to bulk thermal properties.

Diffusion and effusion, graham’s law

Diffusion is the random movement of molecules from regions of higher concentration to regions of lower concentration (down a concentration gradient). Effusion is the escape of gas molecules through a very small opening in a container, also driven by random molecular motion.

Both diffusion and effusion follow Graham’s law, which states that the rate of diffusion or effusion of a gas is inversely proportional to the square root of its molecular weight:

$R a t e_{1} / R a t e_{2} = (M_{2} / M_{1})$

This means that at a given temperature - where all gases have the same average kinetic energy - a lighter gas (lower molecular weight) diffuses or effuses faster than a heavier gas. For example, if two gases are introduced at opposite ends of a tube, the lighter gas travels faster, so they meet closer to the heavier gas’s end.

This law comes from the kinetic theory idea that the average kinetic energy,

$½ m v^{2}$

is the same for all gases at the same temperature. That leads to the velocity relationship:

$v_{1} / v_{2} = (M_{2} / M_{1})$

Deviation of real gas behavior from the Ideal Gas Law, Van der Waals

In an ideal gas, molecules are treated as having negligible volume and no interactions. This works well at low pressure and high temperature, when molecules are far apart.

At higher pressures or lower temperatures, molecules are closer together and begin to experience intermolecular attractions. These attractions pull molecules toward each other and effectively reduce the measured pressure. When molecules are forced extremely close together, their finite size produces steric repulsion, which pushes them apart and increases the pressure.

These deviations from ideal behavior are described by the Van der Waals equation, which includes two constants:

$a$ accounts for attractive forces (lowering the pressure)
$b$ accounts for finite molecular volume (raising the pressure)

Partial pressure, mole fraction, and Dalton’s Law

Partial pressure is the pressure contributed by one gas in a mixture. The total pressure is the sum of the partial pressures of all gases present.

The fraction of the mixture made up by a particular gas is its mole fraction. It’s defined as the moles of that gas divided by the total moles of gas in the mixture.

Dalton’s law states that the partial pressure of a gas equals its mole fraction times the total pressure:

$P_{i} = χ_{i} \cdot Pt o t a l$

This also means the total pressure can be written as the sum of partial pressures:

$Pt o t a l = Σ P_{i} = Σ χ_{i} \cdot Pt o t a l$

This links the composition of a gas mixture directly to its pressure.

Partial pressures of main atmospheric gases at sea level

Absolute temperature, Kelvin scale

Kelvin ( $K$ ) scale starts at absolute zero (no thermal energy)
Conversion: $K = ° C + 273$
Kelvin is essential in science; water freezes at $273 K$ , boils at $373 K$

Pressure, simple mercury barometer

Pressure: $P = \frac{F}{A}$ (force per unit area)
Atmospheric pressure at sea level: $1 a t m = 101 k P a = 760 mm H g = 760 T orr$
Barometer measures atmospheric pressure via mercury column height

Molar volume

1 mole of ideal gas at $0^{\circ} C$ and $1 a t m$ occupies $22.4 L$
1 mole = $6.02 \times 1 0^{23}$ molecules (Avogadro’s number)
Molar volume is $22.4 L / m o l$ at standard conditions

Ideal gas

Ideal gas law: $P V = n RT$
Assumptions: negligible molecular volume, no intermolecular forces
Laws derived:
- Boyle’s law: $P_{1} V_{1} = P_{2} V_{2}$ (constant $T$ )
- Charles’s law: $V \propto T$ (constant $P$ )
- Avogadro’s law: equal volumes = equal moles (same $T$ , $P$ )

Kinetic molecular theory of gases

Gas molecules in constant, random motion
No intermolecular forces, negligible volume, elastic collisions
Pressure from collisions with container walls; temperature = average kinetic energy

Heat capacity at constant volume and at constant pressure

$C_{v}$ : heat needed to raise $T$ by $1^{\circ}$ at constant volume (no work done)
$C_{p}$ : heat needed at constant pressure (includes expansion work; $C_{p} > C_{v}$ )
Boltzmann’s constant links particle kinetic energy to temperature

Diffusion and effusion, Graham’s law

Diffusion: molecules move from high to low concentration
Effusion: gas escapes through small opening
Graham’s law: $R a t e_{1} / R a t e_{2} = M_{2} / M_{1}$
- Lighter gases diffuse/effuse faster

Deviation of real gas behavior from the Ideal Gas Law, Van der Waals

Real gases deviate at high pressure/low temperature
- Intermolecular attractions lower pressure
- Finite molecular size increases pressure
Van der Waals equation:
- $a$ : corrects for attractions
- $b$ : corrects for molecular volume

Partial pressure, mole fraction, and Dalton’s Law

Partial pressure: pressure from one gas in a mixture
Mole fraction: moles of one gas / total moles
Dalton’s law: $P_{i} = χ_{i} \cdot P_{t o t a l}$ ; total pressure = sum of partial pressures

Gas phase